Let me give you some hints on the solutions:
a) Which states of a Kripke structure have some successor lying in the empty state set? (Don't think too much, it's simple)
b) Which states have all their successors in the empty set? (Remember: states that have no successors are also contained in the universal predecessors set!)
c) Which states of a Kripke structure have some predecessor lying in the empty state set? (Don't think too much, again it's simple. Can the condition even be fulfilled?)
d) Which states have all their predecessors in the empty set? (Remember: states that have no predecessors are also contained in the universal successors set!)
For e) to g) it's similar, but with the whole state S instead of the empty set. What I gave you above is basically how to read the simplified set definitions based on the definition on pre and suc of a state (second lines).
I didn't check your definitions in detail, but haven't seen any mistakes so far.
Best regards,
choehne
